What is relation between beta and gamma function?

The beta function ( B(x, y) ) and the gamma function ( \Gamma(z) ) are closely related through the formula ( B(x, y) = \frac{\Gamma(x) \Gamma(y)}{\Gamma(x + y)} ). The beta function can be interpreted as a normalization of the product of two gamma functions. Additionally, the beta function can be expressed as a definite integral, which also reflects its relationship with the gamma function. This connection is particularly useful in various areas of mathematics, including probability and statistics.